Transverse expansion of Bjorken flow in (1+1D) relativistic ideal-magnetohydrodynamics with magnetization

Abstract

We study the evolution of magnetized quark gluon plasma (QGP) in the magneto hydrodynamic (MHD) framework. The fluid under investigation has a non-zero magnetization with infinite electrical conductivity. We solve the coupled Maxwell and conservation equations in (1+1D) transverse flow. We assume that the motion of fluid is longitudinally boost-invariant along beam line.In this study, we consider two different scenarios. First, we consider an ideal relativistic plasma with massless particles and infinite electrical conductivity with a constant magnetic susceptibility (χm). Thus, we solve the coupled Maxwell and conservation equations, and obtain the transverse fluid velocity, the energy density and the magnetic field as functions of both space and time. We investigate the effects of magnetic susceptibility (χm) on the evolution of thermodynamic quantities. Then, we solve the coupled Maxwell and conservation equations with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data [43,44]. We find the evaluation of temperature, energy density, the magnetic field, and the transverse fluid velocity. We improve our previous study [21] to include a nonzero magnetization, the transverse relativistic velocity ux2≠0, and a realistic equation of state.We realize the effects of non-zero magnetization on the fluid quantities are rather small. Besides, our work shows a fluid with a realistic equation and a temperature-dependent magnetic susceptibility behaves like a conformal fluid with a small constant magnetic susceptibility.